Question

A block of copper of unknown mass has an initial temperature of 65.4 ∘C. The copper is immersed in a beaker containing 95.7 g of water at 22.7 ∘C. When the two substances reach thermal equilibrium, the final temperature is 24.2 ∘C. What is the mass of the copper block? Express your answer in grams to three significant figures.

Answer 1

The mass of the copper block: 37,829 g

Further explanation

The law of conservation of energy can be applied to heat changes, i.e. the heat received / absorbed is the same as the heat released

Q in = Q out

Heat can be calculated using the formula:

$\rm \large{\boxed{\bold{Q=m\times c\times \Delta T}}}$

Q = heat, J

m = mass, g

c = specific heat, joules / g ° C

∆T = temperature difference, ° C / K

• 1. H₂O

m = 95.7 g

c = 4.18 J / gºC

delta T = 24.2 °C - 22.7 °C = 1.5 °C

Q H₂O = 95.7 x 4.18 x 1.5

Q H₂O = 600,039 J

• 2. Cu

c = 0.385 J / gºC

delta T = 65.4 °C - 24.2 °C = 41.2 °C

QH₂O = Q Cu

600,039 J = m. 0.385 J / gºC. 41.2. °C

$\rm m=\dfrac{600.039}{0.385\times 41.2}\\\\m=\boxed{37.829\:g}}$

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Answer 2

The mass of the copper block in grams is calculated to be 37.9g

HOW TO CALCULATE MASS IN COLORIMETRY.

• The mass of a substance in colorimetry can be calculated by using the formula below:

Q = m × c × ∆T

Where;

1. Q = amount of heat absorbed or released (J)
2. m = mass of substance (g)
3. c = specific capacity of substance (J/g°C)
4. ∆T = change in temperature (°C)

In this case;

Q(water) = -Q(copper)

m.c.∆T (water) = -m.c∆T (copper)

As given in this question;

FOR WATER:

1. m = 95.7g
2. c = 4.184 J/g°C
3. ∆T = 24.2°C - 22.7°C = 1.5°C

FOR COPPER:

1. m = ?
2. c = 0.385 J/g°C
3. ∆T = 24.2°C - 65.4°C = -41.2°C

m.c.∆T (water) = -m.c∆T (copper)

95.7 × 4.184 × 1.5 = - (m × 0.385 × -41.2)

600.6132 = -(-15.862m)

600.6132 = 15.862m

m = 600.6132 ÷ 15.862

m = 37.9g

• Therefore, the mass of the copper block in grams is calculated to be 37.9g.

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